Consider this peptide:
What is the net charge of this peptide at ph=1
What is the net charge of this peptide at ph=7
To determine net charge on a peptide, you have to look at the pKa value for the different ionizing groups. That's the key.
In considering the structure of this peptide, we need to know what Phe-Glu-Ser-Met means. Peptides are always written with the N-terminal amino acid on the left side. Therefore, the structure is actually N-Phe-Glu-Ser-Met-C.
Knowing this, we can now list all of the ionizable groups in this tetrapeptide. I will use the pKa values on p. 113 of the second edition of Principles of Biochemistry (Lehninger, Nelson, Cox). If the values in your textbook are slightly different than these, that's okay. It shouldn't change the results too much.
There is no ionizable group in the R group in phenylalanine. Therefore, the only ionizable group we need to consider is the N-terminal group. Its pKa is 9.13. (Of course, the COOH group in phenylalanine doesn't exist in the peptide because it's involved in a peptide bond with glutamate.)
Both NH2 and COOH groups in glutamate don't exist because of the peptide bonds with phenylalanine ...